Engineering topics

Kwak, Dochan

Publications and source records attributed to Kwak, Dochan.

211 records · Page 12

NASA NTRS1989

Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

Rogers, Stuart E.↗

NASA NTRS1989

Numerical solution of unsteady incompressible viscous flows in generalized moving coordinate systems

A solution method of the time-accurate, incompressible Navier-Stokes equations in generalized curvilinear moving coordinate systems is presented in this paper. Accuracy is achieved by a conservative finite-volume discretization which satisfies the geometric conservation laws in generalized moving coordinate systems. The solution method is second-order accurate in space and first-order accurate in time. A fractional step solution method is used to efficiently solve the discrete equations. The unknowns, namely the pressure and the volume-fluxes, are chosen to facilitate the formulation of a consistent Poisson equation and to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparisons to other numerical and experimental solutions. The comparisons show good agreement.

Rosenfeld, Moshe↗

NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗

NASA NTRS1989

Numerical simulation of unsteady incompressible viscous flows in generalized coordinate systems

Several numerical solutions of the three-dimensional unsteady incompressible Navier-Stokes equations in generalized coordinate systems are presented. The governing equations are discretized by finite volumes with special care to the accurate approximation of the geometric quantities. The unknowns are the pressure and the volume fluxes over the computational cell faces. This formulation results in a robust fractional step solution method for solving discrete equations. Although this method is formulated for the three-dimensional case, only two-dimensional unsteady results are given. Results are presented for a lid driven two-dimensional cavity flow at Reynolds number of 10,000 and for the flow over a circular cylinder with vortex shedding for several Reynolds numbers in the range 100 less than Re less than 1000.

Rossenfeld, Moshe↗

NASA NTRS1988

An upwind-differencing scheme for the incompressible Navier-Stokes equations

The steady state incompressible Navier-Stokes equations in 2-D are solved numerically using the artificial compressibility formulation. The convective terms are upwind-differenced using a flux difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. Although the current study is limited to steady state problems, it is shown that this entire formulation can be used for solving unsteady problems. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudotime steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square-driven cavity, flow over a backward facing step, and flow around a 2-D circular cylinder.

Rogers, Stuart E.↗

NASA NTRS1988

Numerical simulation of unsteady incompressible viscous flows in generalized coordinate systems

Several numerical solutions of the three dimensional unsteady incompressible Navier-Stokes equations in generalized coordinate systems are presented. The governing equations are discretized by finite volumes with special care to the accurate approximation of the geometric quantities. The unknowns are the pressure and the volume fluxes over the computational cell faces. This formulation results in a robust fractional step solution method for solving discrete equations. Although this method is formulated for the three dimensional case, only two dimensional unsteady results are given. Results are presented for a lid driven two dimensional cavity flow at Reynolds number of 10,000, and for the flow over a circular cylinder with vortex shedding for several Reynolds numbers in the range 100 less than Re less than 1000.

Rosenfeld, Moshe↗

NASA NTRS1988

Artificial dissipation models for hypersonic external flow

Four artificial dissipation models which augment central difference schemes were examined for hypersonic external flows. The models were a first and third order dissipation model, a directionally scaled first and third order dissipation model, a flux limited dissipation model, and a flux difference split dissipation model. Each model was implemented in the lower-upper symmetric-Gauss-Seidel (LU-SGS) algorithm to solve the full Navier-Stokes equations. The latter two models can be regarded as total variation diminishing (TVD) schemes. Test results for model problems showed that the flux limited dissipation model was robust enough to predict a high speed blunt body flow with strong shock and expansion waves. The flux difference split dissipation model was capable of shock capturing with higher resolution, but was less robust. First and third order dissipation models turned out to be neither accurate nor robust enough for high Mach number flow computations.

Yoon, Seokkwan↗

NASA NTRS1988

Numerical study of turbulent internal shear layer flow in an axisymmetric U-duct

This paper presents a simple algebraic turbulence model developed for internal flows which is based on the vorticity length and magnitude. The length scale is defined using the distance between the maximum and the minimum points of the absolute vorticity. This model is numerically tested in a turbulent internal layer flow through an axisymmetric U-duct with very sharp curvature; the ratio of the boundary layer thickness to the radius of curvature of the duct is of order 1. In this U-duct flow, strong adverse and favorable pressure gradients coexist and interact with each other. Satisfactoy agreement with experimental results is obtained.

Chang, James L. C.↗

NASA NTRS1988

A solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method.

Rosenfeld, Moshe↗

NASA NTRS1988

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner in using the method of pseudocompressibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme based on flux-difference splitting is used to compute the convective terms. The upwind differencing is biased based on the sign of the local eigenvalue of the Jacobian matrix. Third-order or fifth-order spatial accuracy is maintained throughout the interior grid points. The equations are solved using an implicit line-relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudotime, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at -90 deg angle-of-attack is also computed.

Rogers, Stuart E.↗

NASA NTRS1987

A Diagonal Algorithm for the Method of Pseudocompressibility

The method of pseudocompressibility has been found to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The computing efficiency of these algorithms are compared. Identical solutions are obtained from both algorithms which compare well with experimental results.

Rogers, Stuart E.↗

NASA NTRS1987

A Navier-Stokes flow simulation of the Space Shuttle Main Engine Hot Gas Manifold

Incompressible viscous flow inside the turnaround duct, the fuel bowl, the transfer duct and the racetrack of the Space Shuttle Main Engine (SSME) Hot Gas Manifold (HGM) has been computed using the method of pseudo-compressibility together with an implicit, approximate-factorization algorithm. A multiple-zone method is used to make solution of flows in complex geometries easy. A model which predicts the pressure loading for the shield and the injector post arrangement without solving the complex flow field in the main injector region is proposed. The computed results show good qualitative agreement with experimental data.

Yang, Ruey-Jen↗

NASA NTRS1987

PIC numerical scheme for a two-dimensional Eulerian code

The present work uses the PIC method with operator splitting to hydroelastoplastic multimaterial flow problems in 2D Eulerian coordinates. The operator splitting procedures are carried out in both Lagrangian and remap phases with alternating direction for each time advancement to maintain the accuracy of one-dimensional scheme. A detail description of the numerical approximations is given with a sample calculation of a tungsten rod penetrating an aluminum target.

Kwak, Dochan↗